Obviously as main Reiki is superior to Jack Frost. But not everyone use some team as main; if you use Water only versus fire, Jack Frost is good. I use water agaisnt my main, fire. Is a very defensive team, Joanne+Sol+Poseidon+Jack Frost. But is not a bad team, and Jack Frost is perfect for the team.
Tiamat's +double is roughly +5-6%, according to a commenter with a sample size of ~277. Double Tiamat got his DA rate to ~20%.
When it comes to choosing from Reiki/Jack Frost/Tiamat as your main:
Reiki's 5% advantage in +water means a higher floor for your offense
Tiamat's +double is for the gamblers/people who really want to up their soul's combo rate cause she's holding back your full bursts :P
Jack Frost is for those leaning defensive against fire (I tend to be in this camp)/have specific defense plans (like if your future 100% damage cut plans rely on eidolon passives)
And then Illuyanka enters the picture not too far into the future. +50% water if you have water eidolons in all your sub slots.
Hmm. If it's 5%, then average attacks goes from 1.14 to 1.24 per turn (from double Tiamat). That's a... ~9% damage increase before we consider synergy with burst generation. The biggest problem here is that if the Soul takes no damage, the amount of turns that you need on average drops from 8,77 to 8,06 - so NOT below 8. That's a huge breakpoint that 5% fails to meet. Thus, there might not be much synergy there. 6% would mean 1.26 attacks per turn, and most importantly, this hits the breakpoint of 7.93 turns per burst.
Meanwhile, 10% elemental attack (from double Reiki) is... in best case scenario ~6% increase. In worst case scenario ~4% (elemental advantage + elemental Relic weapon).
Overall, I'd say that Tiamat is about as good for damage as Reiki is. With Tiamats, your bursts will be slightly weaker, but you might have them slightly more often. And your skills will hit for a bit less.
Personally, I think my water team is pretty stacked (Holy Trinity + Ryu-Oh) but Tiamat is a godsend, even more for Water that lacks Damage, double Tiamat has mathematically a tiny damage edge over double Reiki but still, I'll be using double Jack Frost for Fire content and you most likely should to...
For me the fact that I can blast through Accessory Quest 4 with my Water Team at 7000 HP is kind of mind boggling, even more so the fact that I do this and always finishing at 90+% HP, most of it comes to Jack's Double Damage Resist, so it's nothing to sleep on, personally.
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I'm glad I can easily MLB SSR eidolons now, as I was inactive for Jack Frost and I was only able to get 2 Reikis when she was available, as that was when I started to get serious. I definitely will benefit from Tiamat (who I've already MLB'd). Unfortunately I struggle with level up mats during this time, as I only finished Barong either yesterday or the day before.
As long as you keep spamming half-pots for Gem Quests and spend 100k on Gem Gacha every day, level-up fodder should be fairly easy to obtain.
SR weapons are like slvl20 in two days, though leveling up takes longer (three?). I'd imagine that Eidolons would take like a week.
depends on how strong your team is... 5% water atk might make a difference if you're packing some really high assault... the "meta" players probably got a grid full of assault and pride at SLv20 to make that 5% matter...
Tiamat though... possibly blows those two out the water.... pun not intended...
Tiamat has more atk than most eidolons in the game, ups the rate of double (i'm seeing 5% more chance from comments), and provides a barrier... reiki is just 5% more water attack with around 2/3rds the raw atk as Tiamat and comes with a fire resist, while JF comes with the same things as reiki (more or less), but sometimes removes a charge from bosses and has slightly higher raw atk than reiki...
it's more a case of what you need... in my case, i rolled a ton of defensinve kami and not many offensive ones (hell, my SSR in water element is Aphrodite, Snow Raphael, and Sarasvati). Jack Frost with that pretty much lets me outlast a lot of fire fights and even some off element ones (although my wind and light teams is better for that). i still tend to use reiki as a friend (and sub considering my reiki isn't MLB) but in fire fights, i'm not dying anytime soon...